Control of reflections in transmission lines



Feb. l0, 1948. J. L. LAwsoN CONTROL OF REFLECTIONS IN rITRANSMISSION LINES Filed nec. '-7, 1942 .n.OlUfllm IaTVOT 0.11. Ojll N .liwoillw It? O .ill w 40.0.1 OinlOlvall U 1145.0 .t

mvENToR BY Arrormmrv JAMES :..LAwsQN Patented Feb. l0, 1948 UNITED STATES PATENT OFFICE CONTROL OF REFLECTIONS IN TRANS- MISSION LINES James L. Lawson, Ann Arbor, Mich., assignor to the United States of America,

as represented by the Secretary of the Navy Application December 7, 1942, Serial No. 468,137

18 Claims.

1 This invention relates to transmission lines in which supports of insulating material are provided at spaced points for maintaining the positransmission lines having relatively few support insulators per wave length because the introduction of insulators in addition to'those necessary for mechanica] support increases the loss occurring in the line. Previous to this invention, however, the attempted use of transmission lines having relatively few insulating supports per wave length resulted in great difficulties, because such lines possessed in many cases rather considerable energy reections in theline, and because the input impedances of such lines varied rather widely among dilerent lines not greatly differing in construction. Y Such lines, moreover, showed considerable change of impedance with frequency. It is an object of this invention to provide a transmission line of a type which will operate without undesired energy reection or reactive eilects even though the supporting insulators of the line may be few in number per wave lengths of line. It is a further object of this invention to provide a transmission line having Arelatively few insulating supports per wave length exhibiting desirable transmission characteristics at a particular design Wave length and in addition possessing desirable characteristics at -wave lengths differing somewhat from such design wave lengths in order that small changes in wave length will not greatly. affect the transmission characteristics of the line,

Transmission lines requiring insulating spacers used for the very short wave lengths at which this invention has its main importance are usually transmission lines of. the coaxial conductor type and the invention will 'therefore be illustrated and explained entirely4 with reference-to coaxial conductor transmission lines,y although it is understood that the principles of the invention are also applicable to other types of transmission line using spaced insulating supports, such for instance as parallel wire transmission lines. In its broader aspects the invention also has some applicability to other discontinuities in transmission lines which recur at spaced points such, for

instance, as supporting stubs used in stub-supported transmission line, which stubs may present a slight discontinuity in the line in spite of the efforts that' may be taken to adjust the dimensions of the stub so that no reflections of energy will occur where it is connected to the line. Since insulating supports` are the most common type of 2 recurrent similar discontinuities in transmission lines and since the arrangement of the insulating Support presents the most pressing problem with which the invention is concerned. the invention will be explained with reference to the spacing of insulating supports in a transmission line.`

The invention may best be explained with reference to the drawings in which: Fig. 1 is a cross section of a coaxial conductor transmission line showing two insulating spacers;l

Fig. 2 is a cross section on a reduced scale showing a somewhat longer section of transmission line in which the insulating spacers are regularly spaced;

Fig. 3 is a cross section of a short length of transmission line with insulating support spaced in accordance with this invention;

Fig. 4 is a cross section of a somewhat longer length of transmission line illustrating the posi-v tioning of insulating supports according to this invention, and

Fig. 5 is a diagrammatic cross section on a very much reduced scale of an even longer length of transmission linefor the purpose of illustrating the general system of spacing insulating supports in a transmission line according to this invention.

Fig. 1 shows a short section Y. of transmission line having an inner conductor I and an outer conductor 2 between which are located insulating spacers of the'type generally known as beads, which are shown at 3 and 4. The thickness of the beads is represented by the dimension x1 and the spacing between opposite bead spaces of successive beads is represented by the dimension x2. The dielectric constants of the insulating material of which the beads 3 and 4 are constituted will of course be somewhat `greater than the dielectric constant of air, so that the characteristic impedance of the short section of transmission line which is constituted by that part of the transmission line which embraces the insulating bead will be less than the characteristic impedance of the section-s of transmission line between successive beads. Thus the entire transmission line structure may be considered as a transmission line into which has been interposed at intervals short sections of transmission line of a different characteristic impedance. The interposition of these discontinuities will cause reflections to arise, which is to say that standing waves will occur in the transmission line which will usually vary the input impedance and will also be accompanied by an increased attenuation along the 3 set up by a single bead, except in v`cases where it is desired to consider systems lin which the insulating spacers are of unequal thickness or configuration. Such analysis, moreover, is but a simple application of well-known transmission dielectric constant of the material of the bead line calculation. It is sufficient for the ordinary Y type of transmission line in which all the insulating spacers are essentially similar to consider each insulator as setting up as'ingle re-f 'sultant disturbance consisting essentially of a reflection of some of the incident energy setting up a standing wave, the amount of reflection and consequently the amplitude of the standing wave being determined by the dielectric constant of the material of which the bead is made and also by the thickness of the bead. When there are a number of beads in a transmission line, each will set lup such a disturbance, and since the beads will be at diierent places along the line the phases of the different standing waves set up .can be expected to vary. It will therefore be seen that a certain spacing can be obtained at which the standing waves set up by two dierent beads. such as thebeads 3 and 4 'in Fig. 1, will be in phase opposition .and will Ytherefore cancel, thus promoting transmission of -energy along the transmission line without the production of standing waves. By the use of transmission line calculations I have derived a formula for the vspacing of two insulating beads forming a pair of beads in such a manner that at a desired wave length kthe reflections arising at the two beads will cancel rand the pair of beads will presental minimum or zero disturbance to transmission of energy of such wave lengths along the line. In order that the formula I have derived may be clear yin its meaning., some nf its terms should yfirst be defined with reference to Fig. 1..

As `electrbmagnetic oscillatory energy proceeds along the'transmission line, thel phase ofthe oscillations is of course changing, so that at any given moment there will be a progressive change of phase with position along the lines and of course all points of the line will exhibit a progressive change of phase with time. The progressive change of phase Valong the line `at any given instant will vary with the dielectric constant, so that agreater phase shift per unit length will occur in the sections of line embracing the insulating beads than in the intervening sections of line. The angular phase shift a1 for the Vlength rc1 vwhere the insulating bead is located is given by the formula The relation which I have derived which determines the spacing between the components of .a pair of insulating beads for the cancellation of reflection and standing waves is the following:

V2 r11 L2=i In the above formula :represents the dielectric is given. The formulae apply of course to beads of 'similar dielectric constant and configuration, further calculation being necessary in case the beads are dissimilar. In practice, similar beads are almost always used. Even if for some reason it might be desired to use larger beads at one point of the line, for instance, the beads could easily be arranged lin pairs of similar beads, each pair being spaced according to the above formula.

Examination of the formula expressing the condition for cancellation of reflections from the components of a pair of beads will show that where the bead thickness :r1 is very small, and u1 is consequently also small, the value of the sumof m and a2 will approach an odd multiple of 90, which is to say that the spacing between corresponding spaces of the beads of a pair constituted in the fashion above outlined will be an electrical quarter wave length. The term electrical quarter wave length as just used defines a length somewhat shorter than one quarter of the wave length in air or in air-insulated line, on account of the effects of the dielectric constant of the insulating bead. In the formulae of course the term x refers to the free space wave length.

When the beads are more than a few per cent of the wave lengths in thickness (referring again to the free lspace wavelengths) the approximation that 11+ ai: (Qnsi'li' n being any integer, Vis preferably not used, since better results are obtainable by `calculation using the formula involving the tangent product. The use of that formula and also the extent to which results obtained from it differ from those obtained from the aforementioned approximation in the case of beads having dimensions such as those in common use will readily be seen from the following illustration. Y v

Suppose, for example, that the insulating beads are made of polystyrene having a dielectric constant equal to 2.6 and that each bead has a thickness of 3 per cent of the wave length in air. In this case the formulae determining the spacing will reduce to and the quantities will be defined as follows:

'These calculations, being purely illustrative, have not been carried out to many decimal places. It will be noted that the sum of a1 and an is in this vcase 88.2, which shows to what extent the calculations carried out in this fashion differ from those carried out on the basis of the assumption that ai+a2==90. (For simplicity, spacing in the neighborhood of 270, 450, and so on, has been left out of consideration, though of course such cases follow similar rules.) With bead thicknesses somewhat greater in terms of wave length the difference between and the sum of vai and a will show further increase.

the length of line afa) lwill approach ananas Where, as in the usual case, the transmission line includes more f than two supporting insulators, additional complications are met. If the insulators are arranged in the line as shown in Fig. 2, where they are uniformly spacedv from each other, and if the spacing is then determined as above outlined in order Vthat the reflection from any pair of insulators will cancel out, although the line might behave reasonably well at the exact frequency for which the spacing has been designed to cancel out reections and standing waves, the behavior of the line will be extremely critical with respect to changes in frequency. In practice it is usually desired that the characteristics of the line should remain approximately the same for a small region of frequenoies in the neighborhood of the design frequency. In order that such a conditionV may be obtained further arrangements in the spacing of the insulators are desirable.

Fig. 3 shows in a simple form the arrangement I have devised for obtaining practical cancellation of reflections in a multi-insulator line With- 'out excessive sharpness of the frequency characteristic. In Fig. 3 are shown two pairs of insulating beads 5, and 1, 8 ina coaxiall transmission line. The components of each bead pair are spaced in accordance with the formula above indicated, as shown by the dimensions on Fig. 3 relating to the pair of beads 1, 8. In addition the centers of the respective pairs of beads are spaced from each other in accordance with the same principles used in determining the spacing between individual beads. 'I'he spacing of pairs of insulators from other pairs according tothese principles is in effect a second order correction, so that forv this purpose sufficiently accurate spacing can be obtained with the assumption that a1+a2=90 which, as mentioned before, is suillciently accurate even for the spacing of com# ponents of a pair when vthe insulators are thin. For the purpose of spacing pairs from other pairs, this assumption is suciently accurate for good results for insulators of any reasonable thickness. With this assumption, the spacing of the centers of a pair from the center of another pair reduces to the problem of making the total phase shift angle between such centers an odd multiple of 90.

When the spacing betweenthe centers of the vpairs 5, 6 and 1, 8 is thus determined, the distance between adjacent insulating beads of successive pairs, shown on Fig. 3 by the dimension ma, becomes exactly one quarter wave length greater than the distance' ma which separates the components of the insulator pairs. noted that as an, the bead thickness, becomes small, and avi-a2 as above noted approaches 90, gu-l-as (a: being the phase shift corresponding to 1 80. Thus While :ci-l-zz is equal towslightly less than a quarter wave length, atri-:r3 is equal to slightly less than a half wave length. In the above given example .1:3 would equal 0.48m.

The operation of the arrangement of beads shown in Fig. 3 is believed to be as follows. If because of a slight difference between thei frequency of operation and the design frequency of the line there is a slight resultant reflection from the bead pail-.5, 6,such reflection will be practically cancelled out and in any event greatly reduced, by the opposing reflection set up by the similar pair of beads 1, 8. The degree to which such resultant reflectionswill in factfca'ncel may beexpected to increase with vdecreasing difference llit() It will be Vof spacing between between the frequency ofoperation and thev de-e;

signfrequency of' theline. The spacing of insulator. pairs as just described is also useful in minimizing reflections or standing waves resulting from failure of the spacing within pairs to cancel completely the disturbances set up by the individual insulators even at the` design frequency. Such failure of complete can-` a This principle of spacing groups of beads so a that the resultant reilection from such groupsmay cancel, in the same fashion as it is desired that the reflections from components of a bead pair will cancel, may be .carried further to groups of any size constituted according to the foregoing principle. Thus two groups of beads, each of which group is constituted according to the spac.- ing shown in Fig. 3 (i. i beads in each group) could be spaced in a line with their respective centers separated by the smallest practical num#vv ber of electrical quarter wave lengths, in this case five-fourths wavelengths. (phase angle close to: 450), in which case it Works out that the distance between adjacent beads of the two diiferent four? bead groups will be the same as the distance x2 in Fig. 3. Fig. 4 shows I an arrangement of; 16 insulating beads in a transmission line in accordance with the foregoing principle. In this case two groups of `8 beadsare arranged with their centers approximately eleven-fourths wave lengths apart, each group of 8 beads being conf, stituted of 4 groups of 2 beads with their respective centers separated `by a distance of approximately live-fourthswave lengths and each group of- 4 beads being constituted by 2 pairs of 'beads Withtheir respective centers separated by a dis-- tance roughly equal to three-fourths wave lengths. It will be Iseen from Fig, 4 that the development of larger and larger groups of similar beads according to these principles will result in the spacings between successive beads having always one of two particular values. The symbol O represents the dimension shown on Figs. l and 3 by x2, while the symbol E represents the dimension :r3 of Fig. 3. The scale of the drawing is such that the dimension x1;has been neglected. It should be taken into account as above described -ln spacing the insulators, either through the approximation d1+d2=90, 270 accurate formula given above.

Fig. 5 shows an arrangement of 64 beads in a transmission'line in accordance with the fore-l going principle. In order to show how the spacingsbetween successive beads may be rapidly determined, these spacings are shown in a pattern below the diagrammatic representation of the transmission line. On the uppermost line of this pattern appear thesymbols indicating the length the individual components of the bead pairs whichare intended to function as couplets in accordanceV with vthe principles outlined in connection with Fig. 1. Such a pair may be referred to conveniently as a first order group; On the -second line in the pattern appear symbols indicating the spacings between certain beads which'spacings are determined by the spacing of said couplets into groups of 4 beads functioning in'accordance with the principles described in connection with Fig. 3. Such groups of 4 beads Amay be referred to conveniently as second order groups. On the third line of the pattern appear symbols indicating the spacing between certain etc., or the more` successive beads. which .spacings are determined by the pairing off of groups; oi' 4 beads to form groups of 8 beads, which latter groups may be conveniently referred to as third order groups. Ther fourth, fifth and sixth lines of the pattern show spacings determined byA fourth, fifth and sixth order groupings in the same fashion. The symbol O as in Fig. 4v refers to spacing corresponding to the dimension any in Fig. 3- and the symbol E, alsol as in Fig. 4a, refers to spacing corresponding to the dimension ma' in Fig.` 3. It will be noted that the spacings determined. by second order grouping, i.. e., the spacings between the ends of first order groups, is always given by the dimension E, whereas theA spacings determined by odd order grouping, which is. also the spacings between adjacent ends of even order subgroups, is always given bythe dimension O.. The entire. pattern as developed in Fig.- 5 is symmetrical about the center.

The balancing of groups 4, 8, 16 and so on beads againsteach other in accordance with the prinf cipl'es herein outlined will be seen to result in a spacingr between centers oi two groups which form. a. balanced group of the. next higher order equal to an even multiple of the distance (.rz-i-:cil plus an odd number of quarter wave lengths. The additional quarter wave lengths are brought into the expression for the distance between group centers on account of the :1:3 spacings occrm'ing within the component groups.. Thus the spacing between the center of twol couplets (first order groups) which form a second order balanced group (4 beads) is Mam Corresponding spacings for certain higher orders will be seen to be as follows:

Table Spacing between centers of component groups No. oi beads in comp.

Order oi major component groups groups 3 s Suazo-re? It will be seen that the spacing between balanced group centers for the purpose of forming a balanced group of a higher order may be expressed as where n is the number'of insulators in each of the groups the spacing between the centers of which is to be determined, and m is an odd integer sufficiently large to prevent the said groups of insulators from overlapping. l

The quantity A to which the various calculations in accordance with this invention are referred may be defined as the wave length in air of the oscillations in question A(i. e., those of a frequency for which the transmission line is designed to have its optimum characteristics), 4the wave length in a coaxial transmission line in which there is no insulation other than air being the. same as the wave length of radiation in the open air.

Where the structures producing discontinuities in the line are not simply insulators but are other forms of structures or support forming reflections or standing waves. which it is desired to eliminate, the formula for pairing off such. structures or supports in order to cause reiiections to cancel out as much as possible should be expressed in the more general form:

This is essentially the same formula as that previously given but. it defines the tangent product in terms of the characteristic impedances of the two kinds of sections of the line. Thev previously given formula. will be seen to be a special case 'of the one just given in view of the fact that the formula first given refers to a line of constant conductor dimensions where the only change causing the discontinuity is the introduction of a dielectricA supporting bead, so that. the change in characteristic impedance can be expressed entirely in terms of the dielectric constant (that of air being l). lIn the form of the formula just given, Zr represents the characteristic or surge impedance of the sections of the line within the structure creating the discontinuity, while Z0 represents the characteristic or surgeimpedance of thesections of line making up thev rest of the transmission line. ci and az as before represent the phase shift or electrical length respectively of the sections of line within the discontinuity producing structures and thesections of line between said structures. The relation of a2 to the physical length of the corresponding section of line remains the same as before. In the delnition of e1 the lsquare root of the dielectric constant should be replaced by the more general expression The two expressions are equivalent where the only change in characteristic impedance is that caused by the introduction of dielectric.

The more general formula just discussed, is also convenient for use in transmission lines structure where a change in the dimensions of the conductors of the line takes place at the places where an insulating support is arranged across the line. Once the characteristic impedances of the various parts of the line have beenv calculated in the usual manner, or experimentally determined, the arrangement of a large number of such structures or supports having mutually similar configurations and electrical characteristics can be carried out in accordance with this invention as easily and simply as the distribution of insulators Ain a transmission line as above described.

It will be seen from the description of Fig. 5 that a maximum balancing effect with a given number of beads can be achieved in this fashion with total bead numbers of 2, 4, 8, 16, 32, 64, 126, 256 and so on. For practical purposes, however, it is often desirable to provide lines having a total bead -count different from the foregoing most de sired numbers. Where the design of the apparatus in question. permits some adjustment oi the line length it is desirable to adjust the line length `supporting insulators in the line. `structed according to the foregoing principles,

alieni-rse .so that the number of beads win be a multiple of the highest possible power of 2, `which means that the beads will be grouped as much as pos- 'sible in the larger type of balanced groups. The

llne should not be so cut as to result in its possessing an odd number of beads, since the odd bead in the ordinary case could be expected to set up uncompensated reilections. A line lconstructed as herein described will have a characteristic impedance substantially constant over a range of frequencies, and in fact this characteristie impedance will be substantially that which would be expected in the absence of al1 the supporting insulators. These advantageous properties are not obtainable with an odd number of A line conand, for instance, being constructed such as that of Fig. 5, may be cut without great loss of balancing eiect at some point between diierent rst order couplets, such for instance as at the points :c or y shown on Fig. 5. As mentioned before, the greater degree of balance is to be obtained when the total number of beads is a multiple of a relatively higher power of 2. Indeed if the line fis cut at the points a, b or G, the portionv to the left of the cut will have a maximum degree of balance, the bead arrangement being symmetrical about the middle. VIn general, except for special cases to be ascertained with care, if the line is to be cut a certain amount, greater balance can be obtained by cutting it from o ne end only rather than by trimming both ends.

If the line of Fig.v 5 is cut oil at zc, for instance, it will then include a balanced group of 32 beads covering the length indicated on` Fig. 5 at p, a balanced group of 16 beads occupying the space indicated by q, a group of 4 beads occupying the space r and a couplet occupying the space s. As

ypreviously indicated greater balance could be 'obtained by eliminating the odd couplet s and cutting the line at y, and even greater balance could be obtained byV adding another properly spaced couplet and cutting the line at z so that the 4-bead group r is balanced byan additional ll-bead group. But for many purposes a line cut as indicated at :r might haverquite acceptable transmission characteristics. If a line such as `that of Fig. 5 but cut at the point a: is to be used,

it is to be noted that the spacing between the groups of beads which are not balanced by other groups of beads is no longer material. In other words the spacing between the couplet s and the group r could be varied, and likewise the spacing between the groups p and q and between the groups q and r.l For purpose of practical manufacture, however, it will be convenient to construct lines according to a iixed pattern which is more orV less independent of line length, without attempting to compensate for the presence of couplets or other groups which are not balanced by a similar group paired with them through further adjustmentv of the spacing between such groups and the other groups of beads in the line.

Because of the fact noted above that the characteristic impedance of a line constructed in accordance with the present'invention is substantially the same as if the line were without insulators, insulators may be 'omitted at the ends of the line to provide a more favorable number and grouping of the remaining insulators. For instance, if it should be desired to obtain a length ofthe line of Fig. 5 of such length as would under the scheme ofilig. 5 contain an odd number of nsulators theunpaired insulator on theendof 7:5

fio

moval of insulators in this fashion to obtain bet-y s ter insulator grouping will not disturb the impedance match at the ends of the line.

A further consideration in the grouping of in sulat-ors lies in the circumstance that when the attenuation Within a length of line occupied by a balanced group of insulators as above-described is greater than about three decibels, there is little or no advantage to be gained by any particular adjustment of the spacing between the center of such a group and the center of another balanced group (since the attenuation would then be suiiicient to prevent any eiective degree of cancellation of residual reflections). This considera.,- tion provides a limit beyond which it is normally not useful to carry out the principles of this invention.

For the purpose of ready notation for systems of beads according to the foregoing principles, patterns such as those made up of the symbols O and E appearing in Fig. 5 may be rather cumbersome, particularly after the desired bead configuration has jbeen 'drawn up and it is only a question of giving manufacturing instructions for the construction of a transmission line according to the prearranged design. Since in the arrangements of beads shown in Figs. 3, 4 and 5 only two different spacings occur between successive beads, as above-mentioned, the arrangements of the beads in the line may be denoted by indicating the number of beads in a group in which successive beads are separated by the narrowerspacing. It will be seen from Fig. 5 that when considered in this Way, the beads appear to fall in groups of 2 or 4` beads only, each group being separated by the larger spacings, the beads within the group being separated by the smaller spacings. The numbers appearing above the diagram of the transmission line of Fig. 5 indicate how the spacing of the insulating beads in the line may be designated by a series of numbers representing group size.

The representations of coaxial lines in the drawings are diagrammatic in nature. It is understood that the ratioof the inner diameter of the outer conductor, which is usually called b, to the outer diameter yof the inner conductor, usually called a, is ordinarily chosen in order to provide a desired characteristicline impedance in accordance to the well-known formula:

Z: 10g10 's' With a given culated beforethe above formulae are applied.

Small deviations from the parallel plane shape may, however, be neglected.

Slight changes in thedimension noted on Fig. 3 by the symbol ma' have Va less important effect ig-estarse v'on the transmission characteristic'sof the line lfor diiierent apparatus` involving several Wave lengths within a fairly narrow range, although it is important that the dinienslon :r2 should be adjusted in each case in 'accordance with the principles above voutlined to neutralize reflection at the 'particular frequency 'at Avvhich the line is designed to serve, nevertheless, the dimension :ra can 'conveniently be 'maden the saine for the lines operating lat the several Wave lengths in the said range if '-any 'manufacturing convenience is achieved by this simpli''cation of line specifications. v

By means of ltheV principles above explained transmission lines can be constructed for relatively short Wave lengths, such, for instance, as Wave lengths 'of about 10"'nt'mtfs which there is unusually little attenuation and which exhibits the ordinary characteristics `of a non#- resonant line, sucnas alcsenee ci 'reflections and a reasonably predictable 'inpdanc. When the insulating beads aror'medf high dua'lity pol-ystyrene `v'v'ith a Tthicki'e'ss f fa't olie-#tenth or lone-eighth of an iifeli, losses in the lines 'are q uite W. The spa rig of insulating beads according to `the principles of .this invention -is also useful I flttiig's if() Alllted.

. to ultra-highlrrequcrleytransmissionlines. Thus instead of a 'single bead,- Which inay produce 'undesired reflections, the fitting yinay be y"provided with a pair bead'sspatd iii lidfnee With this invention. A

1. A 'transmission-rer 'electromagnetic waves ojf short Wave l'ngth'in which upp'o'r g insulators substantially similar'to'ech other aiedistributed along its length infsuch a "manner that each of said insulators l'is paired 'with another'and spaced therefromkby a distance'x'z, liasre'd from the nearer 'faces 'of "said insulators, `said insulators being further arrangedfso that each such pair thereof in excess of 'one pair is paired with another pair to form a balancedfgroup of the `second order in which the centers of the component pairs are spaced `by a distance and s0 that each such balanced group of the second order in excess of 'onesuchgroup lis paired with another 'such group to form a balanced second order balancedgroups'beingspaced bya distance form a balanced `group of thenext higher order in Which'the centers of the former'groups are 'spaced by a distance cacca group of the third orden-the 'centers of the said tan a1' tail a'g:

wherein i is the 'Wave length in Vair 'correspond'- ing to thefreduency'for Which said line is designed to have optiinu'm "transmission characteristics; ci is the eireetive asiel thickness of an individuel insulator: e is the dielectric 'constant ofthe ineterial of whichgtherinsulators are Iliade; n is the number of insulators `in each'of the y'groups the spacing between which is to be determined. z'is 'an 'o'dd integerrsuciently large to prevent said groups frnifoverlappiri'g, in is the angular phase shift iiiradiais' occurring in the space "ici ocoup'ie'd by 2in .insulator vand a2 is the angular pl'la's shift in i'adaliisiclirli'ng in the Space-'332 betv'fenins'ul s. v

2. A transmission line lfor 'electromagnetic Waves Of 'short i'vi/ave lengths `vi 1i"vll1ch each JS111)- of similar/ina er'ial, ycoflgu'raton and magnitude and spaced therefrom according 'to 'the 'following formulae:

Allvher'ein A is the wave .length in airf'corresponding to the frequency `for which -said li-ne is designed to have optimum transmission characteristics, :vi is the meandirr'ier'lsion -in vthe direction of said line lofthe' insulators of Kthe pair in question, :t2 is .the -distancebetween the "said insulators Aof-said pair -nieasure'djbtween .their respective rnearer faces, e is the dielectric constant `of the material of which 'the said insulators aremade, i lis the angular phase shift, in radians occurring in Ythe space mi -occupiedby a-n insulator andocjis the angular phase shiftinradians occurring -in -the space e2 between insulators.

A 3. A'trans'lnisslion-line for high-frequencyalterhating currentsin which no -g-'roup of successive insulators 'spaced at -intervals of a quarter lwave vlength or less (said wave llength corresponding to ythe frequency of optir'nufn transmission) lnumbers `inorethanfour insulators-.and in which line each insulator acrossthe line -is--paired withaan-f .other insulator of .similar material, lconfiguration magnitude and spaced thereiromaccording to the followingformulae:r

tan a1 tan a;

fvvherein i Vis "the 'Wave length iin "air 'correspondin question, .rz is the distance between the said insulators of said pair measured-between their respective nearer faces, e is the dielectric constant of the material of which the said insulators are made, ai is the angular phase shift in radians occurring in the space :r1 occupied by an insulator, and az is the angular phase shift in radians occurring in the space :c2 between insulators.

4. A transmission line for high-frequency a1- ternating currents in which the insulators across said line are substantially similar to each other in electric properties and inwhich said insulators are distributed in groups of two insulators and groups of four insulators such that the spacing between the adjacent faces of different insulators of the same group is dened by a distance :c2 and the spacing between diierent groups of insulators, measured from adjacent faces of adjacent insulators of diiierent groups, is defined by a distance ass, the distances x2 and xa being determined by the following relations:

tan a1 tan ri=vhE wherein i is the wave length in air corresponding to the frequency for which the line is designed to have optimum transmission characteristics, :ci is the effective axial thickness of an individual insulator; e is the dielectric constant of the material of which the insulators are made, ai is the angular phase shift in radians occurring in the space x1 occupied by an insulator, and a2 is the angular phase shift in radians occurring in the space between insulators.

5. A transmission line for high-frequency lalternating currents provided with an even number of electrical discontinuity-producing supports of lsimilar electrical characteristics in which line said discontinuity-producing supports are distributed along the length of said line in such a manner that each of said supports is paired with another and spaced therefrom by a distance rc2, measured between adjacent extremities of successive supports, said supports being further arranged so that each such pair thereof in excess of one pair is paired with another pair to form a balanced gro-up yof the second order in which the centers of the component pairs are spaced by a distance and further so that each balanced group of any particular order such that the attenuation in the line including such group is less than 3 decibels, in excess of one such group, is paired With another such group of the same order to form a balancedgroup of the next higher order in which the above distances being deilned by the following formula:

wherein Z1 is the characteristic or surge impedance of the short sections of transmission line at points where the said supports are across the line, Zo is the characteristic or surge impedance of the transmission line where no supports are across the line, ai is the angular phase shift occurring in each section of line constituted by the point at which one of said supports is across the line, and is related to the length of such section of line in the well-known manner, a2 is the angular phase shift occurring in the line in the distance x2 between the components vof any of said terms of insulator, and is related to the said distance :1:2 in the well-known manner, n is the number of such supports in each of the groups the spacing between which is to be determined, and m is an odd integer suiiciently large to prevent said groups from overlapping,

6. A transmission line for high-frequency alternatingcurents having discontinuity-producing structures at various points in said line and in which each of said structures is paired with another of said structures of similar configuration and electrical properties and spaced therefrom according to the following formulae: i

tan a1 tall a2=m2 wherein *A is the wave length in air corresponding to the frequency for which said line is designed to have optimum transmission characteristics, :ri is the length of transmission line involved ineach of the discontinuity-producing structures in question, :r2 is the length of transmission linebetween two similar discontinuityproducing structures paired and spaced in the above manner, Z1 is the characteristic or surge impedance of the sections of transmission lines associated with said discontinuity-producing structure, Zo' is the characteristic or surge impedance of the transmission line between said discontinuity-producing structures, 4au is the angular phase shift in radians occurring in the length of 'transmission line xi occupied by one of said discontinuity-producing structures, and az is the angular phase shift in radians occurring in the length of transmission line :c2 between two similar discontinuity-producing structures paired and spaced in the above manner.

Y7. A transmissionline for high-frequency alternating currents in which discontinuity-producing structures are associated with said line at spaced points, said discontinuity-producing structures being. substantially similar to each other in electrical properties with respect to said transmission line, and in which said discontinuity-producing structures are distributed alongthe length of said transmission line in groups of two structures and groups of-four structures such thatv the lengthof linebetween the adjacent struc- 118111, a1 tan a2 =%2 wherein i is the wavelength in air corresponding to the frequency for. whichsaid line is designed to have optimum transmission characteristics, :nl isthe length of transmissionqline. involved in each of the discontinuity-producing structuresin question, mais the length ofl transmissionv linebetween two similar discontinuity-producing structures` paired and spaced in the above manner, Z1 is the characteristic or surge ilmzredanceof, the sec.- tions of transmission line associated with said discontinuity-producing structure.. Zuis the characteristic. or surge impedance of the transmission line: between said discontinuity-producing. struc-y tures, 1 is the angular phase shift in radians occurringinl the length of transmission line- :c1 oceupied by one of said discontinuity-producing structures, and v@o is thea-ngular phase shift in radians occurring in the length of transmission line :r2 between two similar discontinuity-produclng structures paired and spaced in the above manner.

8. A transmission lne'for high-frequency alternating currents of frequencies in the neighborhood of a particular design frequency, said line having a plurality ofl spacing insulators distributed` along its lengthwhich are substantially similar to each other and which have an, axial dlmension Very small compared with a'quarter wave length corresponding to said,v design frequency,I said insulators being distributed along said line. in such a manner that each. insulator is paired with another insulator located approximately at a distance of an odd number of electrical quarter wave. lengths corresponding to. said, design frequency, said distance being measured from corresponding parts of said insulators, said. insulators being further .arranged so. that each pair thereof in excess of one pair isA paired with another pair to form a balanced group. of the second order in which thel cen-tersof the'component. pairs are spaced by an oddnumber Of: said (111er, ter wave lengths, and so that each balanced group of the second o rder in excess of onev such; balanced group is paired with another group of similar constitution to form a balanced group;l ofv the third order, the centersl offsaid secondi order balanced groupbeing spaced by an'odd'. number of said quarter wave lengths, andso thatv each: balanced group of anyv particular order suchlthat the attenua-tor in the-.line including suchgroup is; less; than three decibels, in excess of one such group, is paired with another balanced group. of 70;

thel same order to form a. balancedagroup. or the next higherk order in which said centers: of the; former groups are spacedbyf an odd number loi.= said quarter wave lengths.

' ing Waves set up 1 6.o hating currents. of frequencies in the. neighbor-' hood' of' a particular design, frequency, said: transf.; mission line having therein. a. plurality of space lng insulators substantially similar to each other inf electrical properties and of an axial dimension small `compared to an electrical. quarter wave length corresponding to said design frequency; said insulators being distributed along said.: line in groups of two insulators and groups of four insulators such that the spacing between cor.- responding parts, of differentinsulators. of the. samegroups is approximately equal. tosaid querter wave length and the spacing between. different groups of insulators measured from; corresponding parts of adjacent insulators.ofdiierentgroups isA approximately equal to an electrical, halfl Wave length corresponding to saidl design frequency.

10. A transmission line for high-frequency alternating currents for transmitting a relatively.- broadv band of frequencies of the order of a particular design frequency in which linespacing lnsulators are distributed in pairs so spaced from each other thatreilections and standing waves set up by one component of any of such pairs are practically cancelled by the reilections and standby the other components of said pairs, at least for said design frequency, said pairs being further arranged so that the resultant reflections and standing waves produced by any of said pairs at frequencies somewhat differing from said design frequency are negatived to a considerable extent,v and to a degree which increases as said last-mentioned frequency approaches said design frequency, by the resultanty reflections and standing waves produced by anotherof said pairs, and in which said pairs and saidy pairs of pairs are organized into balanced groups of higher order forv the purpose of negativing resultant reflections andv standingL waves in a `similar fashion to the extent permitted by' the number of the insulators in said line.

11. A transmission line for high-frequency alternating currents of a particular design frequency in which line insulators are distributed in groups of insulators some' ofV which comprise.

two insulators and others of which groups comprise four insulators, the spacing between insu'- latorsv being such that reflections and standing, waves set up by one insulator will be cancelled to a large extent, at least at said' design frequency. by reilections and standing waves set' up by another insulator paired with said first-mentioned` insulator, said insulators being further spaced: so' that at a frequency somewhat dlfferentfrom said design frequency, resultant reflections and standing waves set up by insulators paired asaforesaid will, to a degree which-increases as said frequency approaches said design frequency, be negatived by the resultant reilection and standing waves set up by another pair of insulators.

12. A transmission line for high-frequency currents of frequenciesv in the neighborhood ofv a particular design frequency in which line insular, tors substantially similar to each other in electrical properties are distributed along the length of said line in accordance with a pattern developed in the following manner:

.O.E.O. .O.E.O. O

wherein a: dot represents they presence-ofan 9, Atransmissionline.for:high-frequencyalter-v F55 insulator, and the symbols O and E- represen? amarsi:

spacings-between adjacent :faces of successiveV insulators determined. in accordance with the following formulae, wherein :I: represents the axial dimensions of the insulator, e represents the dil radians occurring in the 'above-identified space O between insulators:

13. A transmission line for high-frequency currents of frequencies in the neighborhood of a particular design frequency in which line discontinuity-producing support structures substantially similar to each other in electrical properties are distributed along the length of said line in accordance with a pattern developed in the following manner:

'.0.E.0. .O.E.O.

insulator, and a: is the` in accordance with the folteristie or surge impedance of the transmission line where no support structures are across the line, A represents-the wave length corresponding to said design frequency,- i is the angular phase shift in radians occurring in the space occupied by a support structure, and a2 is the angular phase shift in radians occurring inthe laboveidentiied space O between successive support structures:

less than 3 per cent of the wave length in ain Y 18 q t corresponding to said design frequency are distributed along the length of said line in accordance with a pattern developed in the following manner:

..E.o. ono. o

wherein a dot represents the presence of an insulator, and the symbols O and E represent spacings between centers of successive insulators respectively equal to one-quarter and one-half of said wave length.

15. A transmission line for high-frequency alternating-currents for a band of frequencies including a particular design frequency in which line a plurality of insulators substantially similar to each other in electrical properties are distributed along the length of said line in groups. some of which groups comprise two insulators and others of which comprise four insulators, in accordance with the following pattern:

The above pattern of numbers indicating the sequence of two-member and four-member groups, the spacing between the insulators in the same group being defined by. a distance :vz and the spacing between adjacent insulators in different groups being defined by a distance ma, both said distances being measured between the nearer spaces of'successive insulators and being defined by the following relations:

wherein A is the wave length in air correspondingY to the frequency for which the line is designed to have optimum transmission characteristics; :c1 is the effective axial thickness of an individual insulator; e is the dielectric constant of the material of which the insulators are made; ai is the angular phase shift in radians occurring in space :r1 occupied'by an insulator, and an is the angular phase shift in radians occurring in the space x2 above dened.

16. A transmission line of the coaxial conductor type having an inner conductor and a cylindrical outer conductor coaxial therewith and having insulators substantially similar to each other in electric properties supporting said inner conductor relative to said outer conductor, being distributed in said line in groups of two insulators and groups of four insulators such that the spacing between the adjacent faces of different insulators of the same group is defined by a distance ma and the spacing between different groups of insulators, measured from adjacent faces of adjacent insulators of diierent groups, is deie fined by a distance ma, .the distances :r2 and :v3 being determined bythe following relations:

wherein i is the wave lengthk in air corresponding to the frequency for which the line is den -signed to have optimum transmission characteristics; xl is the effective axial thickness of the indivi-dua1 insulators;` e is the dielectric constant of the material of whichthe insulators are made;

ai is the angular phase shift in the radians oc- 1 curring in space x1 occupied by an insulator, and 2 is the angular phase shift in radians occurring in the space me above defined.

17; A transmission line of the coaxial conductor type having an inner `conductor and a cylinp drical outer conductor in which line discontinuity-producing supports are located within said outer conductor at spaced points, said discontinuity-producing structures being substantially similar to each other in electrical properties with i respect to said transmission line, and in which line said discontinuity-producing structures are .distributed along the length-of said transmission line in groups of two structures and groups of four structures such that the length lof'line betan al tan az= wherein 7x is the Wave length air corresponding to the frequency for which said line is vdesigned to have optimum transmission characteristics, mi is the length of transmission line involved in each of the discontinuity-producing structures in question, x2 is the length of-trans- Vmission line between two similar discontinuityproducing structures paired and spaced in the above manner, Z1 is the characteristic or surge impedance of the sections of transmission line associated with said discontinuity-producing structure, Zo is the characteristic or surge impedance of the transmission line between said discontinuity-producing structure, mi is the angular phase shift in the radians occurring in space x1 above defined, and az is the angular phase shift in radians occurring in the space :v2 above defined.

18'. A transmission line of the coaxial conductor type for frequencies in the neighborhood of a particular design frequency, said transmisison line having an inner conductor, a, cylindrical outer conductor coaxial with said inner conductor, and having within said outer conductor a plurality of spacing insulators substantially similar to each other in electrical properties and of an axial dimension small compared to an elec.- trical quarter wave length corresponding to said design frequency, said insulators serving tosupport said inner conductor relative to said outer conductor being distributed along said line in groups of two insulators and groups .of four insulators such that the spacing between corresponding parts of diierent insulators of the same groups is approximately equal vto said .quarter wave length and the spacing between different groups of insulators measured from corresponding parts of adjacent insulators of different groups is approximately equal to an electric half wave length corresponding to said design frequency.

JAMES L. LAWsoNf REFERENCES CITED The following references are of record in the leof this patent.:

UNITED STATES PATENTS Number Name Date Cork July 11, 1939 Scheldorf Jan. 13, 1942 

